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a cat is walking on the keyboard. Given that the cat walked just on letters (with an equal chance for each letter A-Z) and wrote a 6-letter word, what is the probability that this word is a palindrome.

Nurlan Cabbarlı
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    Welcome to MSE! What have you tried? Do you have any ideas of your own? We can help you better once we understand exactly where you're struggling ^_^ – HallaSurvivor Dec 13 '20 at 07:57
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    Since each letter is equally likely, the answer is independent of the first 3 letters. So go ahead and assume that the first 3 letters are A-B-C, and then analyze from there. – user2661923 Dec 13 '20 at 08:03

1 Answers1

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Let XYZ be the first 3 letters.

The probability that the fourth letter is Z is $1/26$. The probability that the fifth letter is Y is $1/26$ and the probability of the sixth letter being X is $1/26$ as well.

So the probability of your word being a palindrome is $1/26^3$

michalis vazaios
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